The invention is based on a fuel injection pump of the general type having a main pump piston and an intermediate piston actuated in synchronism with fuel injection. During the intervals between injections, one end of the intermediate piston is exposed to a supply pump, which positively displaces fuel during the upward half of its stroke into a relief conduit. After the reversal of a control apparatus the intermediate piston is exposed on its rear face to the fuel of a high-pressure pump, which supplies the fuel to a fuel injection nozzle. In terms of adapting the principle of injection to engine manufacturers' requirements for optimizing such engine characteristics as fuel consumption, noise, exhaust emissions and the like, a known fuel injection pump of this general type has quite substantial limitations, which are both structurally imposed and caused by variations in temperature.